Setting camera to position where it can render a seamless repetable orthographic scene
The trick with Orthographic cameras in Blender is that they use a specific scale system, such that 1 Blender unit always matches the largest dimension of the render output.

That means if you are rendering an image of $1920\times1080$ with a scale factor of $1$ then $1920$ pixels in your image will match exactly one Blender scene unit.

If the image is say $2048\times4096$ with a scale of $2$ that means that $4096$ pixels will match exactly two Blender units.

That being said in your case you need to do some math.

Place you camera such that it points exactly at the center point C midway between your two marker empties $A$ and $B$, while being rotated exactly an angle of $45°$ in the X axis. Distance is unimportant.



You can select both empties $A$ and $B$ and easily place the 3D cursor to the selection with Cursor to Selected, and then use the operator Center View to Cursor to center the camera between the two.

Now determine the distance between the two empties $[AB]$. Since it forms a right-angled triangle, with the distance being its hypotenuse, then the exact scale of the camera will be the square root of this distance. In my example above they dist exactly two units apart, so $\sqrt{2} = 1,4142$ will be exactly the scale factor you must place in the orthographic camera.